Spatial and temporal variation in algal-assemblage structure in isolated dryland river waterholes, Cooper Creek and Warrego River, Australia

The scale at which algal biodiversity is partitioned across the landscape, and the biophysical processes and biotic interactions which shape these communities in dryland river refugia was studied on two occasions from 30 sites in two Australian dryland rivers. Despite the waterholes studied having characteristically high levels of abiogenic turbidity, a total of 186 planktonic microalgae, 253 benthic diatom and 62 macroalgal species were recorded. The phytoplankton communities were dominated by flagellated cryptophytes, euglenophytes and chlorophytes, the diatom communities by cosmopolitan taxa known to tolerate wide environmental conditions, and the macroalgal communities by filamentous cyanobacteria. All algal communities showed significant differences between catchments and sampling times, with a suite of between 5 and 12 taxa responsible for similar to 50% of the observed change. In general, algal assemblage patterns were poorly correlated with the measured environmental variables. Phytoplankton and diatom assemblage patterns were weakly correlated with several waterhole geomorphic measures, whereas macroalgal assemblage patterns showed some association with variability in ionic concentration.

A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons

We introduce a general Hamiltonian describing coherent superpositions of Cooper pairs and condensed molecular bosons. For particular choices of the coupling parameters, the model is integrable. One integrable manifold, as well as the Bethe ansatz solution, was found by Dukelsky et al. [J. Dukelsky, G.G. Dussel, C. Esebbag, S. Pittel, Phys. Rev. Lett. 93 (2004) 050403]. Here we show that there is a second integrable manifold, established using the boundary quantum inverse scattering method. In this manner we obtain the exact solution by means of the algebraic Bethe ansatz. In the case where the Cooper pair energies are degenerate we examine the relationship between the spectrum of these integrable Hamiltonians and the quasi-exactly solvable spectrum of particular Schrodinger operators. For the solution we derive here the potential of the Schrodinger operator is given in terms of hyperbolic functions. For the solution derived by Dukelsky et al., loc. cit. the potential is sextic and the wavefunctions obey PT-symmetric boundary conditions. This latter case provides a novel example of an integrable Hermitian Hamiltonian acting on a Fock space whose states map into a Hilbert space of PE-symmetric wavefunctions defined on a contour in the complex plane. (c) 2006 Elsevier B.V. All rights reserved.